Acousto-optic deflector with multiple output beams

ABSTRACT

Optical apparatus includes an acousto-optic medium and an array of multiple piezoelectric transducers attached to the acousto-optic medium. A drive circuit is coupled to apply to the piezoelectric transducers respective drive signals including at least first and second frequency components at different, respective first and second frequencies and with different, respective phase offsets for the first and second frequency components at each of the multiple piezoelectric transducers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Divisional of U.S. application Ser. No. 15/524,282 filed May4, 2017 which is a 371 National Stage of PCT/IL2015/051068 filed Nov. 5,2015 and which claims benefit of priority to U.S. application Ser. No.62/078,450 filed Nov. 12, 2014. The entire disclosures of the priorapplications are considered part of the disclosure of the accompanyingdivisional application, and are hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates generally to optical devices and systems,and particularly to acousto-optic devices.

BACKGROUND

Acousto-optic devices use sound waves to diffract light. In a typicaldevice of this sort, a transducer, such as a piezoelectric transducer,is attached to an acousto-optic medium, typically a suitable transparentcrystal or glass. The transducer is driven by an electrical signal tovibrate at a certain frequency, and thus creates sound waves in theacousto-optic medium. The expansion and compression of the acousto-opticmedium due to the sound waves modulate the local index of refraction andthus create a grating structure within the medium, with a perioddetermined by the frequency of the drive signal. A beam of light that isincident on this grating will thus be diffracted as it passes throughthe device.

Various types of acousto-optic devices are known in the art.Acousto-optic deflectors, for example, use the diffraction of theincident beam to steer the angle of the output beam. The angle ofdeflection of the output beam depends on the period of the gratingstructure in the acousto-optic material and may thus be adjusted byappropriately varying the drive signal frequency.

Acousto-optic deflectors may be driven with a multi-frequency drivesignal in order to diffract the incident beam into multiple output beamsat different, respective angles. Further details of this sort ofmulti-frequency drive are described, for example, by Hecht in“Multifrequency Acoustooptic Diffraction,” IEEE Transactions on Sonicsand Ultrasonics SU-24, pages 7-18 (1977), which is incorporated hereinby reference; and by Antonov et al. in “Efficient Multiple-Beam BraggAcoustooptic Diffraction with Phase Optimization of a MultifrequencyAcoustic Wave,” Technical Physics 52:8, pages 1053-1060 (2007), which islikewise incorporated herein by reference.

Acousto-optic devices with multiple output beams have also beendescribed in the patent literature. For example, U.S. Pat. No. 5,890,789describes a multi-beam emitting device, which splits a light beamemitted from a light source into a plurality of beams using an opticalwaveguide-type acousto-optic element or the like, driven with aplurality of electric signals with different frequencies. As anotherexample, U.S. Patent Application Publication 2009/0073544 describes adevice for the optical splitting and modulation of monochromaticcoherent electromagnetic radiation, in which an acousto-optical elementsplits the beam generated by a beam source into a number of partialbeams. An acousto-optical modulator disposed downstream of theacousto-optical element is fed the split partial beams and driven withadditional high-frequency electrical signals.

As still another example, U.S. Pat. No. 5,255,257 describes anelectronic circuit that is said to allow an acousto-optic deflector tobe used in multi-frequency mode at high power levels with a minimumamount of intermodulation between each frequency. Reduction ofinterference between multiple separate signal frequencies is achieved byprecise control of the individual phasing of each separate frequencyrelative to a common reference frequency. The relative phase of eachfrequency is also controlled so that a low maximum power is achieved forthe combined signal that is presented to the acousto-optic deflectorwithout decreasing the overall average power of the multiple signalfrequencies.

SUMMARY

Embodiments of the present invention provide improved devices andmethods for optical deflection.

There is therefore provided, in accordance with an embodiment of thepresent invention, optical apparatus, which includes an acousto-opticmedium and an array of multiple piezoelectric transducers attached tothe acousto-optic medium. A drive circuit is coupled to apply to thepiezoelectric transducers respective drive signals including at leastfirst and second frequency components at different, respective first andsecond frequencies and with different, respective phase offsets for thefirst and second frequency components at each of the multiplepiezoelectric transducers.

Typically, the respective phase offsets at the first and secondfrequencies are chosen so that acoustic waves at the first and secondfrequencies propagate through the acousto-optic medium with different,respective first and second wavefront angles. In a disclosed embodiment,the acousto-optic medium is configured to receive an input beam ofradiation and to split the input beam into at least first and secondoutput beams at respective first and second beam angles determined bythe first and second frequencies, wherein the first and second wavefrontangles are chosen so as to satisfy respective Bragg conditions at thefirst and second beam angles.

In some embodiments, the drive signals applied by the drive circuitfurther include at least a third frequency component, at a thirdfrequency, with a different phase offset from the first and secondfrequency components. The at least first, second and third frequenciesmay define a Golomb ruler.

In a disclosed embodiment, the drive signals applied by the drivecircuit further include one or more harmonic frequency components,having respective amplitudes and phases chosen so as to cancel harmonicwaves generated at a multiple of at least one of the first and secondfrequencies in the acousto-optic medium due to at least one of the firstand second frequency components.

In some embodiments, the apparatus includes a radiation source, which isconfigured to direct an input beam of radiation to be incident on theacousto-optic medium, wherein the acousto-optic medium is configured tosplit the input beam into multiple output beams at respective beamangles determined by the respective frequencies of the at least firstand second frequency components. The at least first and second frequencycomponents of the drive signals may have different, respectiveamplitudes that are chosen so that the multiple output beams have equalrespective intensities.

There is also provided, in accordance with an embodiment of the presentinvention, optical apparatus, which includes an acousto-optic medium,which is configured to receive an input beam of radiation, and at leastone piezoelectric transducer attached to the acousto-optic medium. Adrive circuit is coupled to apply to the at least one piezoelectrictransducer a drive signal including at least three frequency components,having respective frequencies that define a Golomb ruler and areselected so as to cause the acousto-optic medium to split the input beaminto multiple output beams at respective beam angles determined by therespective frequencies.

The drive signal applied by the drive circuit may further include one ormore harmonic frequency components, having respective amplitudes andphases chosen so as to cancel harmonic waves generated at a multiple ofat least one of the respective frequencies of the at least threefrequency components in the acousto-optic medium. Additionally oralternatively, the at least three frequency components of the drivesignal may have different, respective amplitudes that are chosen so thatthe multiple output beams have equal respective intensities.

There is additionally provided, in accordance with an embodiment of thepresent invention, optical apparatus, which includes an acousto-opticmedium, which is configured to receive an input beam of radiation, andat least one piezoelectric transducer attached to the acousto-opticmedium. A drive circuit is coupled to apply to the at least onepiezoelectric transducer a drive signal including multiple frequencycomponents, which include at least first and second fundamentalcomponents, at respective first and second fundamental frequencies,which are selected so as to cause the acousto-optic medium to split theinput beam into first and second output beams at respective beam anglesdetermined by the first and second fundamental frequencies, and one ormore harmonic frequency components, having respective amplitudes andphases chosen so as to cancel harmonic waves at respective multiples ofthe fundamental frequencies in the acousto-optic medium.

There is further provided, in accordance with an embodiment of thepresent invention, an optical method, which includes directing an inputbeam of radiation to be incident on an acousto-optic medium, to which anarray of multiple piezoelectric transducers is attached. Respectivedrive signals are applied to the piezoelectric transducers, including atleast first and second frequency components at different, respectivefirst and second frequencies and with different, respective phaseoffsets for the first and second frequency components at each of themultiple piezoelectric transducers, so as to cause the acousto-opticmedium to split the input beam into at least first and second outputbeams at respective beam angles determined by the respective first andsecond frequencies.

There is moreover provided, in accordance with an embodiment of thepresent invention, an optical method, which includes directing an inputbeam of radiation to be incident on an acousto-optic medium, to which atleast one piezoelectric transducer is attached. A drive signal isapplied to the at least one piezoelectric transducer, including at leastthree frequency components, having respective frequencies that define aGolomb ruler and are selected so as to cause the acousto-optic medium tosplit the input beam into multiple output beams at respective beamangles determined by the respective frequencies.

There is furthermore provided, in accordance with an embodiment of thepresent invention, an optical method, which includes directing an inputbeam of radiation to be incident on an acousto-optic medium, to which atleast one piezoelectric transducer is attached. A drive signal isapplied to the at least one piezoelectric transducer, including multiplefrequency components, which include at least first and secondfundamental components, at respective first and second fundamentalfrequencies, which are selected so as to cause the acousto-optic mediumto split the input beam into first and second output beams at respectivebeam angles determined by the first and second fundamental frequencies,and one or more harmonic frequency components, having respectiveamplitudes and phases chosen so as to cancel harmonic waves atrespective multiples of the fundamental frequencies in the acousto-opticmedium.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic, pictorial illustration of a multi-beam deflectionsystem, in accordance with an embodiment of the present invention;

FIG. 2 is a schematic sectional view of an acousto-optic deflector usedin generating multiple output beams, in accordance with an embodiment ofthe present invention;

FIG. 3 is a schematic sectional view of an acousto-optic deflectordriven by a phased array of transducers, in accordance with anembodiment of the present invention;

FIG. 4 is a block diagram that schematically illustrates amulti-frequency drive circuit for an acousto-optic deflector, inaccordance with an embodiment of the present invention;

FIGS. 5A-5E are plots that schematically illustrate intensity variationsamong the output beams of a multi-beam acousto-optic deflector, inaccordance with an embodiment of the present invention;

FIG. 6 is a plot that schematically illustrates phase delays applied toan array of transducers, in accordance with an embodiment of the presentinvention;

FIG. 7 is a plot that schematically shows a frequency spectrum of anacousto-optic deflector that is driven in accordance with an embodimentof the present invention; and

FIG. 8 is a flow chart that schematically illustrates a method forequalization of intensity among multiple output beams from anacousto-optic deflector, in accordance with an embodiment of the presentinvention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

Because of their high speed and angular range, acousto-optic devices arean attractive means for generating and deflecting multiple beams ofoptical radiation, using a single input radiation source. Such deviceshave not been widely adopted in practice, however, in large part due toproblems of low diffraction efficiency and nonlinearities in theacousto-optic response of the modulator. These nonlinearities result ingeneration of waves in the acousto-optic modulator at harmonics of thedrive frequencies and at sum and difference frequencies, leading to lossof beam power to undesired diffraction orders and poor control over thepower levels of the different output beams.

Embodiments of the present invention that are described herein addressthese problems and thus enable an acousto-optic device to generatemultiple output beams with high efficiency and precise control over thepower distributed to the output beams. In the disclosed embodiments,such a device comprises an acousto-optic medium, which receives an inputbeam of radiation, and at least one piezoelectric transducer attached tothe acousto-optic medium. A drive circuit applies to the piezoelectrictransducer (or transducers) a drive signal comprising multiple frequencycomponents having novel, advantageous properties. In the disclosedembodiments, the drive signal comprises multiple fundamental componentsat respective fundamental frequencies, which are selected so as to causethe acousto-optic medium to split the input beam into multiple outputbeams at respective beam angles that are determined by the correspondingfundamental frequencies. These frequencies in the drive signal may bemodulated in order to steer the output beams.

In some embodiments, in order to obviate problems arising fromnonlinearities, as explained above, the drive signal also comprisesharmonic frequency components, having respective amplitudes and phaseschosen so as to cancel harmonic waves at multiples of the fundamentalfrequencies in the acousto-optic medium. As a result, energy from theinput beam that would otherwise be lost to parasitic beams at undesiredangles due to such harmonic waves is channeled into the desired outputbeams instead.

Additionally or alternatively, this sort of signal cancellationtechnique may be applied to suppress parasitic diffraction at anglescorresponding to sums and differences of the fundamental frequencies.When the fundamental frequencies are evenly spaced, however, or evenrandomly spaced, certain sum and difference frequencies may coincidewith one or more of the fundamental frequencies, leading to variationsin amplitude among the output beams that are difficult to control. Inorder to ensure that the sum and difference frequencies are wellseparated from the fundamental frequencies, the fundamental frequenciesare chosen in some embodiments of the present invention so as to definea Golomb ruler, in which no two pairs of frequencies are the samedistance apart.

In some embodiments, an array of multiple piezoelectric transducers isattached to the acousto-optic medium and is driven as a phased array.For this purpose, the drive circuit applies drive signals comprisingcomponents at the various frequencies, as described above, withdifferent, respective phase offsets for the different frequencycomponents at each of the multiple transducers. These phase offsets aretypically chosen so that acoustic waves at the different frequenciespropagate through the acousto-optic medium with different, respectivewavefront angles. The wavefront angles may be chosen (by appropriatechoice of phase offsets) so that the multiple output beams, with theirdifferent, respective beam angles, satisfy respective Bragg conditionsat these beam angles.

System Description

FIG. 1 is a schematic, pictorial illustration of a multi-beam deflectionsystem 20, in accordance with an embodiment of the present invention. Aradiation source, such as a laser 22, emits a single input beam 23 ofoptical radiation, pulsed or continuous, which may comprise visible,ultraviolet or infrared radiation. Input beam 23 is incident on anacousto-optic deflector 24, which splits the input beam into multipleoutput beams 30. A drive circuit 28 (also referred to simply as a“driver”) applies a multi-frequency drive signal to one or morepiezoelectric transducers 26, which drive deflector 24 in order togenerate acoustic waves in the acousto-optic medium that split the inputbeam into multiple output beams 30. Deflector 24 may comprise anysuitable acousto-optic medium that is known in the art, includingcrystalline materials such as quartz, tellurium dioxide (TeO₂),germanium, or glass materials such as fused silica or chalcogenideglasses. Crystalline media may be cut along specific, preferred crystaldirections to obtain the desired acousto-optic properties, in terms ofsound velocity and birefringence, for example. Transducers 26 maysimilarly comprise one or more pieces of any suitable piezoelectricmaterial, such as lithium niobate, which are typically attached to theacousto-optic medium via a metal bonding layer. Details of the operationof drive circuit 28 and of the drive signals that it generates arepresented in the figures that follow and the description below.

In the pictured embodiment, a scanning mirror 32 scans output beams 30over a target surface 36 via a scan lens 34. This sort of arrangementcan be used in a variety of applications, such as multi-beam laserdrilling and printing. Although only a single mirror 32 is shown in thisfigure, alternative embodiments (not shown in the figures) may employdual-axis mirrors, which may be scanned together or independently,and/or any other suitable type of beam scanner that is known in the art.In an alternative embodiment, two acousto-optic deflectors may bedeployed in series, one of which splits input beam 23 into multipleoutput beams, which are separated along a first direction, while theother scans the beams in the orthogonal direction. All such embodimentsmay take advantage of the multi-frequency drive schemes described hereinand are considered to be within the scope of the present invention.

FIG. 2 is a schematic sectional view of acousto-optic deflector 24, inaccordance with an embodiment of the present invention. This figureillustrates the effect and operation of the multi-frequency driveprovided by drive circuit 28 and piezoelectric transducer 26. Themulti-frequency drive signal from drive circuit 28 causes piezoelectrictransducer 26 to generate acoustic waves at the multiple drivefrequencies, which propagate through the acousto-optic medium indeflector 24. Each of the different drive frequencies establishes anacousto-optic diffraction grating in the crystal at a correspondingspatial frequency, i.e., the crystal contains multiple superposedgratings of different spatial frequencies. When input beam 23 entersdeflector 24, each of the gratings in the deflector diffracts the inputbeam at a different angle, depending on the grating frequency. Thus,deflector 24 splits input beam 23 into multiple output beams 30 atdifferent angles θ₁, θ₂, . . . , corresponding to the differentfrequencies f₁, f₂, . . . . Optics 34 focus the output beams to form acorresponding array of spots 1, 2, . . . , on target surface 36. Bymodulating the amplitudes of the signals at the correspondingfrequencies, in appropriate synchronization with the pulses of inputbeam 23, drive circuit 26 may control the intensity of the correspondingoutput beams 30 generated by each pulse of the input beam. Moreparticularly, drive circuit 28 may turn the corresponding frequencycomponents on and off in order to choose the combination of output beams30 to generate at each pulse. Additionally or alternatively, drivecircuit 26 may modulate the component frequencies f₁, f₂, . . . , inorder to modulate the corresponding angles θ₁, θ₂, . . . , and thuschange the locations of the spots on surface 36.

FIG. 3 is a schematic sectional view of acousto-optic deflector 24 witha phased array of transducers 40 attached to the acousto-optic medium ofthe deflector, in accordance with an embodiment of the presentinvention. Although transducer is shown in the preceding figures as aunitary block, in practice all embodiments of the present invention maybe implemented in this manner, using an array of transducers 40.

Drive circuit 28 is pictured conceptually as comprising a frequencygenerator 42, which drives transducers 40 through respective phaseshifters 44, so that the signal is fed to the transducers withdifferent, respective phase offsets. As a result, the wavefronts ofacoustic waves 46 that propagate through the acoustic medium ofdeflector 24 are not parallel to the face of the medium to whichtransducers 40 are attached. The wavefront angle is typically chosen, byappropriate setting of phase shifters 44, so that the angle θ betweeninput beam 23 and the wavefront satisfies the Bragg condition for thegiven drive frequency, i.e., sin θ=nλ/2d, wherein λ is the wavelength ofthe input beam, n is the diffraction order (typically n=1), and d is thewavelength of the acoustic waves at the given frequency. This choice ofwavefront angle enhances the efficiency of diffraction by deflector 24,particularly at frequencies away from f₀ (the frequency at which thephase difference between adjacent channels is zero) where a passivedelay line cannot match well the phase difference. Criteria for settingphase offsets between adjacent transducers are described furtherhereinbelow with reference to FIG. 6.

In the embodiments disclosed herein, drive circuit 28 applies respectivedrive multi-frequency signals to piezoelectric transducers 40, withfrequency components at multiple different frequencies. For each ofthese frequencies, the Bragg condition results in a differentdiffraction angle. Therefore, for optimal performance of deflector 24 atall frequencies, phase shifters 44 apply a different phase offset foreach frequency at each of transducers 40. Consequently, acoustic waves46 at the frequencies propagate through the acousto-optic medium withdifferent, respective wavefront angles, which are chosen so as tosatisfy respective Bragg conditions for the corresponding frequenciesf₁, f₂, . . . , . . . and deflection angles θ₁, θ₂, . . . , of thecorresponding output beams 30.

FIG. 4 is a block diagram that schematically illustrates functionalcomponents of drive circuit 28 for acousto-optic deflector 24, inaccordance with an embodiment of the present invention. The digitalcomponents of drive circuit 28 may typically be implemented inhard-wired or programmable logic, such as in a programmable gate array.Although the blocks in FIG. 4 are shown as separate components for thesake of conceptual clarity, in practice the functions of thesecomponents may be combined in a single logic device. Alternatively, atleast some of the digital components of circuit 28 may be implemented insoftware running on a computer or dedicated microprocessor.

A frequency selection block 50 selects a number of fundamentalfrequencies f₁, f₂, . . . , to be applied in driving deflector 24, inorder to generate output beams 30 with corresponding deflection anglesθ₁, θ₂, . . . . If the output beam angles are to be scanned transversely(as in system 20, shown in FIG. 1), block 50 may be programmed tomodulate each of these frequencies over time by an amount up to ±Δf,resulting in angular scanning of each beam by up to ±Δθ. Thus,typically, block 50 generates a sequence of frequency vectors, eachvector comprising a number m of fundamental frequency values{f_(i)+δf_(i)} that are to be applied to deflector 24 at a particulartime in order to generate m output beams 30 at corresponding angles{θ_(i)+δθ_(i)}, wherein δf_(i) and δθ_(i) are frequency and anglevariations within the ranges ±Δf and ±Δθ, respectively. In practice,there are potentially N_(max) separate output beams in the overallfrequency range ΔF of system 20, wherein N_(max)=ΔF*D/V_(S) (wherein Dis the optical aperture, and V_(S) is the sound velocity in theacousto-medium). The frequency shift ±Δf is the range between twoadjacent frequencies (ΔF=2Δf*N_(max)). Typically, m sub-beams areselected within the array of the N_(max) possible beams.

FIGS. 5A-5E are plots that schematically illustrates intensityvariations among output beams 30 of acousto-optic deflector 24, whichare generated in accordance with embodiments of the present invention.These plots illustrate the effect of frequency nonlinearities indeflector 24 on the respective intensities of the output beams, whereinthe effect is quantified on the vertical axis in the figure in terms ofthe ratio between the variance (standard deviation—STD) of the outputbeam intensities relative to the mean intensity of the output beams. Thehorizontal axis shows the fundamental frequencies that are generated byfrequency selection block 50 in various frequency selection schemes, allof which include ten fundamental frequencies. Alternatively, larger orsmaller numbers of fundamental frequencies may be used. The variances inthe plots were obtained by testing the beam intensities for the set ofchosen frequencies many times, with randomly-chosen phases associatedwith each frequency in the set.

Bars 62 in FIG. 5A show the intensity variances when a set ofevenly-spaced fundamental frequencies is used, with relative smallintervals (approximately 2 MHz) between adjacent frequencies. Sum anddifference effects among the different frequencies result in enhancementof some frequencies at the expense of others, so that the relativeintensities of output beams 30 vary widely, by as much as 100%. Thissort of uncontrolled intensity variation is unsuitable in manymulti-beam industrial applications. The severity of the problem can bereduced by spreading the frequencies farther apart, as illustrated bybars 64, at intervals of approximately 6 MHz, as shown in FIG. 5B, butsubstantial intensity variations among the beams still remain.

Bars 66 and 68 in FIGS. 5C and 5D illustrate another approach, in whichthe fundamental frequencies are spread over the available range (60-120MHz in the present example) at random intervals. This approach reducesthe intensity variances among output beams 30 to less than about 20%,but this level of variation is still too high for precisionapplications.

In the scheme illustrated by bars 70 in FIG. 5E, the fundamentalfrequencies are chosen so as to define a Golomb ruler, meaning that notwo pairs of frequencies are the same distance apart. The ruler isdefined over the N_(max) available resolution points of system 20, whichare spaced apart by ΔF/(N_(max)−1). Because of this distribution of thefrequencies, sums and differences of any given pair of fundamentalfrequencies will not coincide with the respective sum or difference ofany other pair of fundamental frequencies, and combinations offundamental frequencies of the forms 2*f1−f2 or f1+f2−f3 will notcoincide with any other fundamental frequency, but will rather fallwithin the intervals between bars 70. Therefore, as shown in FIG. 5E,the intensity variations between output beams 30 are less than about 2%.This is just one example of a 10-beam ruler selected from among theN_(max) available output beams, and other m-beam rulers can be definedthat will meet these criteria, with different distributions of rulerfrequencies. Furthermore, parasitic waves in acousto-optic deflector 24at the sum and difference frequencies of the ruler frequencies may becanceled in a manner similar to the harmonic cancellation techniquesdescribed below, by addition of frequency components at the sum anddifference frequencies with respective amplitudes and phases chosen soas to cancel the parasitic waves at these frequencies.

Returning now to FIG. 4, the set of frequencies selected by block 50 issupplemented by a harmonic cancellation block 52. As explained above,nonlinearities in the acousto-optic medium of deflector 24 give rise toharmonic waves at multiples of the fundamental frequencies, and possiblyalso waves at intermediate frequencies given by the sums and differencesbetween the fundamental frequencies. These nonlinear components have aparasitic effect on the performance of deflector 24, since they creategrating components in the deflector that cause a portion of the energyof input beam 23 to be diffracted at undesired angles.

Block 52 addresses this problem by adding corrective harmonic frequencycomponents to the frequency vector generated by block 50. The respectiveamplitudes and phases of these corrective components are chosen so as tocancel the parasitic (harmonic and sum/difference) waves in theacousto-optic medium. Specifically, block 52 computes the expectedamplitudes and phases of the parasitic waves, and adds in correctivecomponents of the same amplitudes at the parasitic frequencies, but withopposite phase. The amplitudes and phases of the corrective componentsmay be computed a priori, based on a mathematic model of the behavior ofdeflector 24, or they may be set empirically. In either case, the netresult will be a substantial reduction in the amplitudes of the gratingcomponents in the acousto-optic medium at the parasitic frequencies, andthus diversion of a greater portion of the input beam energy into outputbeams 30 in the desired angular directions.

A phase adjustment block 54 generates multiple streams of time-domainsamples corresponding to the frequency components provided by blocks 50and 54. Each stream is directed to a respective one of transducers 40and contains the same frequency components, but with different,respective phase offsets. These phase offsets are chosen according tothe desired wavefront angle of acoustic waves 46 in deflector 24 at eachfrequency. Typically, the relative phase offsets between the samplestreams are not uniform over the entire frequency range, but ratherincrease with frequency, so that the wavefront angles likewise increasewith frequency, in order to satisfy the Bragg condition at eachfrequency as explained above.

Specifically, block 54 may set the phase offsets at the differentfrequencies is according to the following formula:

${\Delta\;{\varphi(f)}} = {\frac{2{\pi \cdot S \cdot \lambda}}{V_{s}^{2}} \cdot {f( {f_{0} - f} )}}$

In this equation:

Δφ(f) is the phase difference between two adjacent output channels ofblock 54 at frequency f;

S is the distance between the centers of adjacent transducers 40;

λ is the optical beam wavelength;

V_(S) is the acoustic velocity in the acousto-optic medium; and

f₀ is the applied frequency that gives zero phase difference betweenadjacent channels and satisfies the Bragg condition for the opticaloutput beam.

FIG. 6 is a plot that schematically illustrates phase delays applied byblock 54 to transducers 40, in accordance with an embodiment of thepresent invention. A curve 72 in the figure represents the actual,measured phase delay as a function of frequency, with f₀=200 MHz. Forcomparison, a line 74 shows the phase delay as a function of frequencyfor a fixed, one-meter delay line. The benefit of thefrequency-dependent phase adjustment provided by block 54 is apparentparticularly at high frequencies.

Referring back to FIG. 4, blocks 50, 52 and 54 are typically implementedin digital logic and/or software, as explained above. The digital samplestreams from block 54 are input to respective channels of amulti-channel digital/analog converter 56, which generates correspondingoutput signals to drive transducers 40. Assuming appropriate choice ofthe frequency components and phase offsets, the transducers willgenerate a superposition of acoustic waves in deflector 24, at differentfundamental frequencies and with different wavefront angles, whileparasitic waves generated by nonlinear processes in the acousto-opticmedium will be suppressed.

FIG. 7 is a plot that schematically shows a frequency spectrum ofacousto-optic deflector 24 when driven in accordance with embodiments ofthe present invention. Specifically, the plot shows the efficiency ofdiffraction of the deflector (i.e., the percentage of the availableenergy from input beam 23 that is diffracted at the desired angle) as afunction of the drive frequency of the deflector.

A first curve 80 shows the baseline diffraction efficiency, whendeflector 24 is driven without harmonic cancellation and with phasedelay between transducers 40 set by a fixed delay line (i.e., withblocks 52 and 54 inactive). A second curve shows the effect of wavefrontangle adjustment by phase adjustment (block 54), which enhances thediffraction efficiency primarily, although not exclusively, at higherfrequencies. A third curve 84 shows the enhancement of efficiency,primarily at low frequencies, due to active harmonic cancellation byblock 52. The net result is an enhancement of the effective bandwidth ofdeflector 24 by about 50%.

FIG. 8 is a flow chart that schematically illustrates a method forequalization of intensity among output beams 30 from acousto-opticdeflector 24, in accordance with an embodiment of the present invention.In many applications of system 20, such as laser printing and machining,it is important that output beams 30 have respective intensities thatare equal (to within a predefined tolerance). The method of FIG. 8 maybe applied by driver 28 in setting the relative amplitudes of thefrequency components of the drive signal in order to satisfy thiscriterion. Although these settings may be made a priori, based on acalculated model, in practice it is generally preferable to measure theactual intensities of the generated output beams 30 using a suitablemeasurement device (for example, a camera, not shown in the figures) asan input to the present equalization algorithm in the calibration phase.The method of FIG. 8 may be performed for each non-empty subset ofpossible drive frequencies out of the set of ruler frequencies. For eachsuch subset, a sequence of solutions is generated, wherein each solutiongenerates a set of equalized-intensity output beams with slightlystronger intensities than the beams generated by the previous solution,in an iterative process. In other words, each successive solution usesthe previous solution as a starting point. The intensities are expressedin terms of their diffraction efficiency, and list of targetefficiencies, E (for the successive iterations), is provided as an inputto the process, along with the permitted solution tolerance Δ.

The calculation begins at the smallest target intensity (or efficiency),with the frequency components of the drive signal set to equal, smallamplitudes. Drive circuit 28 applies a drive signal having a vector of mamplitudes X₀ at the m different frequency components, and themeasurement device measures a vector M of the respective opticalintensities of the m output beams 30, at a measurement step 90. Aprocessor (not shown) computes the average efficiency M_(avg) over M(i.e., over all beams), and evaluates the deviation of each of theefficiencies in M from M_(avg), at an efficiency evaluation step 92.

If the maximum deviation computed at step 92 is greater than Δ, anadditional measurement M_(p) is taken with the input amplitudes set to[X₀·(1+δ)], and another measurement M_(m) is taken with the inputamplitudes set to [X₀·(1−δ)], at an incremental measurement step 94.(Here δ is a small increment, which depends on the amount of noise inthe measurement process, for example, δ=0.05). The processor then fits alinear model for each beam separately, given the measured intensities(M_(p), M_(m)) and the relative change from X₀, and solves the model foreach beam i to find the relative change u_(i) that should generate thetarget efficiency E, at a modeling step 96. (Alternatively, a largernumber of measurements may be taken at step 94, and the processor maythen compute a higher-order model, such as a quadratic model.) Taking Uto be the vector of all the calculated changes u_(i), the processorcomputes the vector X₀⊗U (wherein the multiplication is done separatelyfor each beam), at an amplitude update step 98. The result is used asthe amplitude vector X₀ for the next iteration through step 90.

When the maximum deviation of the measured intensities in M from M_(avg)is found at step 92 to be less than Δ, the processor checks the currentsolution X₀ to determine whether M is within the tolerance Δ from thetarget efficiency, E, for the current iteration, at an efficiencyevaluation step 100. If the solution is not within the tolerance Δ fromE, then the current amplitude vector X₀ is updated according, forexample to the value X₀·√{square root over (E/M_(avg))}, at an amplitudeupdate step 102. (Alternatively, other update factors may be used atthis step, such as different exponents of E/M_(avg).) The process thenreturns again to step 90.

When M is found at step 100 to be within Δ of E, the processor checkswhether the entire list of target efficiencies E has been reached, at alist checking step 104. In not, the current vector X₀ becomes thestarting point for the next iteration through the preceding steps, withE set to the next target efficiency in the list, at an efficiency updatestep 106. When the last efficiency value in the list has been reached,the equalization process ends, at a termination step 108. If anunrealistic target efficiency is chosen, however, the process may failbefore reaching step 108.

It will be appreciated that the embodiments described above are cited byway of example, and that the present invention is not limited to whathas been particularly shown and described hereinabove. Rather, the scopeof the present invention includes both combinations and subcombinationsof the various features described hereinabove, as well as variations andmodifications thereof which would occur to persons skilled in the artupon reading the foregoing description and which are not disclosed inthe prior art.

The invention claimed is:
 1. Optical apparatus, comprising: anacousto-optic medium, which is configured to receive an input beam ofradiation; at least one piezoelectric transducer attached to theacousto-optic medium; and a drive circuit, which is coupled to apply tothe at least one piezoelectric transducer a drive signal comprising atleast three frequency components, having respective frequencies thatdefine a Golomb ruler and are selected so as to cause the acousto-opticmedium to split the input beam into multiple output beams at respectivebeam angles determined by the respective frequencies, wherein the drivesignal applied by the drive circuit further comprises one or moreharmonic frequency components, having respective amplitudes and phaseschosen so as to cancel harmonic waves generated at a multiple of atleast one of the respective frequencies of the at least three frequencycomponents in the acousto-optic medium.
 2. The apparatus according toclaim 1, wherein the at least three frequency components of the drivesignal have different, respective amplitudes that are chosen so that themultiple output beams have equal respective intensities.
 3. Opticalapparatus, comprising: an acousto-optic medium, which is configured toreceive an input beam of radiation; at least one piezoelectrictransducer attached to the acousto-optic medium; and a drive circuit,which is coupled to apply to the at least one piezoelectric transducer adrive signal comprising multiple frequency components, which comprise atleast: first and second fundamental components, at respective first andsecond fundamental frequencies, which are selected so as to cause theacousto-optic medium to split the input beam into first and secondoutput beams at respective beam angles determined by the first andsecond fundamental frequencies; and one or more harmonic frequencycomponents, having respective amplitudes and phases chosen so as tocancel harmonic waves at respective multiples of the fundamentalfrequencies in the acousto-optic medium.
 4. An optical method,comprising: directing an input beam of radiation to be incident on anacousto-optic medium, to which at least one piezoelectric transducer isattached; and applying to the at least one piezoelectric transducer adrive signal comprising at least three frequency components, havingrespective frequencies that define a Golomb ruler and are selected so asto cause the acousto-optic medium to split the input beam into multipleoutput beams at respective beam angles determined by the respectivefrequencies, wherein applying the drive signal further comprisesapplying one or more harmonic frequency components, having respectiveamplitudes and phases chosen so as to cancel harmonic waves generated ata multiple of at least one of the respective frequencies of the at leastthree frequency components in the acousto-optic medium.
 5. The methodaccording to claim 4, wherein applying the drive signal comprisessetting the at least three frequency components of the drive signal tohave different, respective amplitudes that are chosen so that themultiple output beams have equal respective intensities.
 6. An opticalmethod, comprising: directing an input beam of radiation to be incidenton an acousto-optic medium, to which at least one piezoelectrictransducer is attached; and applying to the at least one piezoelectrictransducer a drive signal comprising multiple frequency components,which comprise at least: first and second fundamental components, atrespective first and second fundamental frequencies, which are selectedso as to cause the acousto-optic medium to split the input beam intofirst and second output beams at respective beam angles determined bythe first and second fundamental frequencies; and one or more harmonicfrequency components, having respective amplitudes and phases chosen soas to cancel harmonic waves at respective multiples of the fundamentalfrequencies in the acousto-optic medium.